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The Cryptoclub: using Mathematics to Make and Break Secret Codes

Janet Beissinger and Vera Pless
A K Peters
Publication Date: 
Number of Pages: 
[Reviewed by
Sarah Boslaugh
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Julius Caesar is said to have used a primitive type of encryption, now called the Caesar cipher, to send coded messages to his generals. The same encryption method was used by the broadcasters of the 1930s radio programs Little Orphan Annie and Captain Midnight to send encoded messages which listeners, if equipped with a Radio Orphan Annie Secret Society Decoder Pin or Captain Midnight Code-o-Graph respectively, could decipher. These examples demonstrate two major purposes of cryptography: to communicate only with the people you wish to receive your message, and to have fun creating and solving puzzles. The two purposes overlap as well: part of the fun of using secret codes is feeling smarter than people who don't know how to decipher the messages.

The Cryptoclub was written, with support from a grant from the National Science Foundation, to introduce cryptography to middle-school students, and to use their interest in secret codes to introduce mathematical ideas such as modular arithmetic and prime factorization in the context of encrypting and decrypting messages. The first code discussed is the Caesar cipher, a simple code created by shifting the letter of the alphabet by a certain number of spaces; for instance in a Caesar shift of three, plaintext a = ciphertext D, plaintext b = ciphertext E and so on, so the plaintext word "dog" becomes the ciphertext "GRJ". Of course such a simple method of encryption is easily broken, as certain Confederate generals discovered to their chagrin during the Civil War, and The Cryptoclub demonstrates this process by a fictional cast of middle school students (boys and girls are included equally, let it be noted) who send and decrypt each other's messages.

The Cryptoclub presents a number of different systems of encryption and methods of breaking them: for instance simple substitution ciphers are easily broken using relative frequency tables for letters of the English alphabet. Other methods of encryption presented include the Vignere Cipher, multiplicative ciphers, Affine ciphers, and public key ciphers. Each type of cipher is presented in detail and exercises are included allowing students to apply the techniques presented. The Cryptoclub also includes short descriptions of famous examples of secret codes, including the Beale Ciphers, the Zimmerman telegram, and the German Enigma cipher.

The Cryptoclub is intended for middle-school students, and could be used for classroom teaching or as a supplemental or recreational book for students interested in cryptography. However, the potential appeal is much broader: the simplest ciphers could be solved by a child in grade school, and much of The Cryptoclub can be enjoyed by adults as well.

Janet Beissinger is a Research Assistant Professor in the Department of Mathematics, Statistics and Computer Science at the University of Illinois at Chicago and is the co-author of Math Trailblazers, a mathematics curriculum for grades K-5. Vera Pless is a Professor in the Department of Mathematics, Statistics and Computer Science at the University of Illinois at Chicago and has published over 115 papers on coding and discrete mathematics. A webpage for The Cryptoclub, which includes puzzles and games and allows users to post their own encrypted messages, is available at

Sarah Boslaugh, PhD, MPH, ( is a Performance Review Analyst in the Center for Healthcare Quality and Effectiveness at BJC HealthCare in St. Louis, MO. She wrote An Intermediate Guide to SPSS Programming: Using Syntax for Data Management for Sage Publications in 2005 and is currently writing Secondary Data Sources for Public Health: A Practical Guide for Cambridge University Press. She is also Editor-in-Chief of The Encyclopedia of Epidemiology which will be published by Sage in 2007.

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